A273950 Prime factors of generalized Fermat numbers of the form 12^(2^m) + 1 with m >= 0.

5, 13, 17, 29, 89, 97, 233, 257, 769, 36097, 40961, 65537, 81281, 153953, 163841, 260753, 1724417, 4550657, 5767169, 8253953, 11304961, 13631489, 21495809, 69619841, 77651969, 147849217, 158334977, 159522817, 1711276033, 6528575489, 27286044673, 52613349377

Offset: 1

Author

Arkadiusz Wesolowski, Jun 05 2016

Keywords

• nonn

Comments

Primes p such that the multiplicative order of 12 (mod p) is a power of 2.

References

• Hans Riesel, Common prime factors of the numbers A_n=a^(2^n)+1, BIT 9 (1969), pp. 264-269.

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 1..44
• Anders Björn and Hans Riesel, Factors of generalized Fermat numbers, Math. Comp. 67 (1998), no. 221, pp. 441-446.
• Anders Björn and Hans Riesel, Table errata to “Factors of generalized Fermat numbers”, Math. Comp. 74 (2005), no. 252, p. 2099.
• Anders Björn and Hans Riesel, Table errata 2 to "Factors of generalized Fermat numbers", Math. Comp. 80 (2011), pp. 1865-1866.
• C. K. Caldwell, Top Twenty page, Generalized Fermat Divisors (base=12)
• Harvey Dubner and Wilfrid Keller, Factors of Generalized Fermat Numbers, Math. Comp. 64 (1995), no. 209, pp. 397-405.
• OEIS Wiki, Generalized Fermat numbers

Crossrefs

Cf. A023394, A072982, A152585, A268660, A268664, A273945 (base 3), A273946 (base 5), A273947 (base 6), A273948 (base 7), A273949 (base 11).

Programs

Mathematica

Select[Prime@Range[2, 10^5], IntegerQ@Log[2, MultiplicativeOrder[12, #]] &]